Principal and complementary series representations at the late-time boundary of de Sitter

TL;DR

This paper links free massive scalar fields in de Sitter space to principal and complementary series representations of SO(d+1,1) by analyzing late-time operators and their two-point functions.

Contribution

It introduces late-time operators in de Sitter space and demonstrates their correspondence to specific group representations, providing new insights into the structure of quantum fields in cosmology.

Findings

Scalar fields correspond to principal and complementary series representations.

Late-time operators' two-point functions match group representation structures.

Provides a framework for understanding quantum fields in de Sitter space.

Abstract

We demonstrate how free massive scalar fields in the set up that usually appears in early universe inflationary studies, correspond to the principal series and complementary series representations of the group SO(d+1,1) by introducing late-time operators and computing their two-point functions.